Mixed membership stochastic blockmodels

TLDR

Observations of pairwise relationships arise in many domains such as protein interactions, gene regulation, email exchanges, and social networks, but probabilistic modeling is difficult because standard exchangeability assumptions fail. The paper introduces the mixed membership stochastic blockmodel, a latent variable model for relational data. The model extends traditional blockmodels to allow mixed membership, yielding low‑dimensional representations of objects, and is fitted via a fast variational inference algorithm applied to social and protein interaction networks.

Abstract

Observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing such data with probabilisic models can be delicate because the simple exchangeability assumptions underlying many boilerplate models no longer hold. In this paper, we describe a latent variable model of such data called the mixed membership stochastic blockmodel. This model extends blockmodels for relational data to ones which capture mixed membership latent relational structure, thus providing an object-specific low-dimensional representation. We develop a general variational inference algorithm for fast approximate posterior inference. We explore applications to social and protein interaction networks.